73.1.26 problem 2.4 (d)

Internal problem ID [15004]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.4 (d)
Date solved : Tuesday, January 28, 2025 at 07:27:22 AM
CAS classification : [_quadrature]

\begin{align*} x y^{\prime }+2&=\sqrt {x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

dsolve([x*diff(y(x),x)+2=sqrt(x),y(1) = 6],y(x), singsol=all)
 

\[ y = -2 \ln \left (x \right )+2 \sqrt {x}+4 \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 18

DSolve[{x*D[y[x],x]+2==Sqrt[x],{y[1]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \left (\sqrt {x}-\log (x)+2\right ) \]